Now, for each directed graph of mutations \(\mathrm {m}({\bf x})\) , we can associate a graph \(\mathrm {M}({\bf x})\)  on the same set of vertices \(V(\mathrm {m})\) .
Corresponding to each directed edge of \(\mathrm {m}\) , there is an edge of \(\mathrm {M}\)  with the same ends (loops being excluded).
In this sense, the graph \(\mathrm {M}({\bf x})\)  is the underlying (simple) graph of the directed graph \(\mathrm {m}({\bf x})\) .
That is, the graphs without self- and directed-edges so that when several edges (mutations) connect the genotype \({\bf x}\)  with the same accessible-mutant \({\bf x}^{\prime }\) , only one (undirected) edge is kept.
Thus, every directed graph \(\mathrm {m}({\bf x})\)  defines a unique, up to isomorphism, reduced graph \(\mathrm {M}({\bf x})\) 
(see the mathematical definition in [1]}).
Now it is natural to do the union of each graph \(\mathrm {M}({\bf x})\) , to describe how genotypes can be reached from somewhere in the genotype space in one mutation operation.
We call this object the mutational network. It is defined as:
\(\mathcal {M}(\mathcal {X}):=\bigcup _{{\bf x}\in \mathcal {X}} \mathrm {M}({\bf x}).\) 
